Where to start: Scrap all your ideas and start over.
Yes, everything you asked for can be done. The reality is though is that, with the amount of complexity you are asking for, you will be a full time sysadmin for them - you might as well quit your day job now.
Your setup is simply too complex for a non-techie (and to be honest, as a techie, I don't want to have to admin something that complex at home). You need to stop asking "can I" and ask "should I?"
Windows PCs joined to active directory can let you manage them, set logon hours, etc.
Why do you care to know if the PCs are sleeping/on/off/whatever?
A router running DD-WRT will let you deny internet access based on hours and/or PCs in a simple manner. To be perfectly honest, I hate the concept of internet filtering (by parents or otherwise) as I believe it is another step toward turning people into drones, rather than teaching them to think for themselves, so I'm not even going to offer any suggestions on that subject.
I agree with the other posters, the system you have suggested will end as follows:
1. The kids will learn how to hack around it. This can be a good thing or bad thing, depending on your point of view
2. The system is so complex it will never work and the parent will never use it as they have no clue
3. You will grow to hate it as it will take too much of your time.